Related papers: Piecewise Analytic Subactions for Analytic Dynamic…
We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its…
We study the analyticity properties of the free energy $f_\ga(m)$ of the Kac model at points of first order phase transition, in the van der Waals limit $\ga\searrow 0$. We show that there exists an inverse temperature $\beta_0$ and…
In this paper, for any positive integer $\ell\geq2,$ we define $\ell$-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\mathbb{C}.$ Further, we compute a possible list of singularities…
Denote by $T$ the transformation $T(x)= 2 \,x $ (mod 1). Given a potential $A:S^1 \to \mathbb{R}$ we are interested in exhibiting in several examples the explicit expression for the calibrated subaction $V: S^1 \to \mathbb{R}$ for $A$. The…
It is well known that any power series over a finite field represents a rational function if and only if its sequence of coefficients is ultimately periodic. The famous Christol's Theorem states that a power series over a finite field is…
In the framework of the 1/N-expansion we show that the Callan-Symanzik beta- function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This behavior can be interpreted by…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
$\beta$-functions for abelian and non-abelian gauge theories are studied in the regime where the large $N$ flavor expansion is applicable. The first nontrivial order in the 1/$N$ expansion is known for any value of $N\alpha$, and there are…
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $\phi(\partial\Omega)$ of a reference set…
We discuss a general result of holomorphic extension of a real analytic function $f$ defined on the boundary $\partial D$ of a real analytic strictly convex subset $D\subset\subset \C^n$. We show that this follows from the hypothesis of…
From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit $\beta$ and the greedy $\beta$-transformation. In this paper, we consider different…
We consider a generalized Takagi function for beta-expansions with the base $1<\beta\leq2$, motivated by multifractal analysis for digit frequency sets of beta-expansions [20]. We show that it is pointwise $\alpha$-H\"older continuous for…
We study the asymptotic expansion in $n$ for the partition function of $\beta$ matrix models with real analytic potentials in the multi-cut regime up to the $O(n^{-1})$ terms. As a result, we find the limit of the generating functional of…
The Riemann Xi-function Xi(t)=xi(1/2+it) is a particularly interesting member of a broad family of entire functions which can be expanded in terms of symmetrized Pochhammer polynomials depending on a certain scaling parameter beta. An…
Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…
We present a study of the problem of finiteness of the $\beta$-expansions for the set of natural numbers, condition $F_1$ in brief, for three families of Pisot numbers for which the $\beta$-expansion of 1 is not a non-decreasing sequence.…
We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of convergence (which is a ball B(0,R) centered at 0). At each…
Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…
We consider a family of potentials f, derived from the Hofbauer potentials, on the symbolic space Omega=\{0,1\}^\mathbb{N} and the shift mapping $\sigma$ acting on it. A Ruelle operator framework is employed to show there is a phase…
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…